Collective Dynamics of Deterministic and Noisy Oscillator Populations: Beyond Ott-Antonsen Theory

振子系综中的同步表现为宏观集体模的出现。在特定情况下，这种模式可以通过奥特-安东森方法进行分析描述。我们在这个项目中的第一个目标是通过在奥特-安东森流形附近构建一个有效的摄动理论来推广这种方法，从而将其扩展到非理想情况。我们将用这个理论探讨奥特-安东森方程没有涵盖的影响：内在噪声的影响，确定性高次扰动的影响，参数的无序。我们的第二个目标是研究共噪声对耦合振荡器同步特性的影响。主要的注意力将集中在耦合是不同步的，从而与噪声的同步作用竞争的情况。虽然分析理论将为最简单的设置开发，但效果也将在实际相关的系统上进行测试，如约瑟夫森结和自旋扭矩振荡器。

Synchronization in ensembles of oscillators manifests itself as appearance of a macroscopic collective mode. In a particular situation, such a mode can be described analytically by virtue of the Ott-Antonsen approach. Our first aim in this project is to generalise this approach by constructing an effective perturbation theory near the Ott-Antonsen manifold, thus extending it to non-ideal situations. We will explore with this theory the effects which are not covered by the Ott-Antonsen equations: effects of intrinsic noise, of deterministic high-harmonics perturbations, of disorder in parameters. Our second goal is to study effects of common noise on the synchronization properties of coupled oscillators. The main attention will be devoted to situations where coupling is desynchronizing and thus competes with synchronizing action of noise. While analytical theory will be developed for simplest setups, the effects will be also tested on practically relevant systems like Josephson junctions and spin-torque oscillators.